A middle school took all of its 6th grade students on a field trip to see a symphony at a theater that has 4100 seats. The students filled 2296 of the seats in the theater. What percentage of the seats in the theater were filled by the 6th graders on the trip?

a = amount invested at 6%

how much is 6% of "a"? (6/100) * "a", namely 0.06a.

b = amount invested at 4%

how much is 4% of "b"? (4/100) * "b", namely 0.04b.

we also know that the yielded amount in interest or the annual income he's got from both is $116, so if we simply add their interest, that'd be 0.06a + 0.04b = 116.

We also know that he invested 400 more in "b" than in "a", so whatever "a" might be, we know that b = a + 400.

[tex]0.06a~~ + ~~0.04(\stackrel{b}{a+400})~~ = ~~116\implies 0.06a+0.04a+16=116 \\\\\\ 0.10a+16=116\implies 0.10a=100\implies a=\cfrac{100}{0.10} \\\\\\ \boxed{a=1000}\hspace{5em}\stackrel{1000+400}{\boxed{b=1400}}[/tex]

The expression for the function f(x) in standard form if the function f(x) is divided by x-2 is f(x) = 3x³ + 2x² - 20x + 17.

The function that when divided by 2x + 1, the quotient is x² - 8x + 8 and the remainder is 5 is determined as follows:

f(x) = (2x + 1)(x² - 8x + 8) + 5

Simplifying the above gives the following:

f(x) = 2x³ - 16x² + 16x + x² - 8x + 8 + 5

f(x) = 3x³ - 15x² + 8x + 13

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Answer:

1 or 0

Step-by-step explanation:

in order for a number's square equals to itself, it has to be 1 or 0.

Answer: 3 - 2x

Step-by-step explanation:

Product = Multiplication

Product of 2 and x = 2*x

3 minus 2x

3-2x

Answer:

3−2×x or 3-(2xx)

Reason:

The 6x-x on the right hand side simplifies to 5x

This means the right hand side turns into 5x-11, which is an identical copy of the 5x-11 on the left side.

The equation 5x-11 = 5x-11 has infinitely many solutions because we can replace x with any real number to end up with a true statement.

Answer:

If angle ABD = 60°, then angle BDC can be found using the fact that the measures of the angles in a triangle add up to 180°.

So, m(angle BDC) = 180 - (m(angle ABD) + m(angle BDA))

Therefore, m(angle BDC) = 180 - (60 + m(angle BDA))

So the measure of angle BDC is not fixed, it depends on the measure of angle BDA.

The simplified expressions that we have are;

a) 2∛16 - 12

b) (-375)^1/3x^8/3y^8/3

The term simplifications means that we have to write the expression is the easiest way that it can be written. In this case we have two expressions. We can be able to simplify them as we work through the steps that have been written below;

8) -2∛81 + 2∛16 - 2∛81

-4∛81 + 2∛16

-4(3) + 2∛16

2∛16 - 12

10) ∛-375x^8y^8

This simplifies to;

(-375)^1/3x^8/3y^8/3

This is the way that we can be able to simplify the expressions here.

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Answer:

(A+7)^4

Step-by-step explanation:

The equation that relates velocity, distance and time is given as follows:

v = 171/2.

The relation between velocity, distance and time states that the velocity is obtained by the quotient of the distance by the time, as follows:

v = d/t.

In which:

The parameters for this problem are given as follows:

d = 171, t = 2.

Hence the equation that gives the velocity in miles per hour is of:

v = 171/2.

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Answer:

3 1/10 as a fraction

Step-by-step explanation:

3.3 as a fraction is 3 3/10. The first 3 is a whole number because it is to the left of the decimal point, and it represents 3 ''ones''. However, the second 3 to the right of the decimal point represents a decimal amount. Because this 3 is in the tenths place, we say it as ''3 tenths.

33 is repeating

    When converting a percent in fraction form, you must know its place value of each number, and you can easily transform it to fraction.

3.3% - the place value is ones. It is a whole number and called as three.

3.3% - the place value is tenths. It is called as three-tenths.

When you convert a percent to decimal, you must divide it by 100.

3.3 ÷ 100

The probability that the first two people to leave are science teachers is; 2/15

The parameters about the subject teachers are;

Number of maths teachers = 5

Number of Science Teachers = 6

Number of Social Studies Teachers = 5

Total number of teachers = 5 + 6 + 5

Total teachers = 16

Thus;

Probability that first to leave is a science teacher = 6/15

Probability that after the first leaves, the second to leave will be a science teacher = 5/15

Thus;

P(first two to leave are science teachers) = (6/15) * (5/15)

= 2/15

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The conclusion of the proportion is if a and bare not coprime, when it share a factor greater than 1

Here we have given that if and are not coprime that is share a factor greater than.

And we need to find the examples that contradict the conclusions of proposition.
While we looking into the given question, we have identified that  if and  are not coprime.

In order to find the conclusion to this one, we must know the definition of co prime.

The term co prime is referred as those umbers that do not have any common factor other than 1.

As per the definition, we have clearly know that if the two number has the factor greater than one then it will not a co prime to each other.

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To complete the square, you would add (16/2)^2 = 64/4 = 16 to both sides of the equation.

x ax2 + bx + c = 0 is a quadratic equation, which is a 2nd quadratic formula in a single variable. a 0. It has at most one solution since it is a 2nd polynomials equation, which is guaranteed by the algebraic fundamental theorem.

In other terms, you have a quadratic equation if a times the squares of the equation after b plus b twice that the same phrase not square plus c equals 0. The initial equation will change to a quadratic equation if the value in the () is replaced with such a variable like t.

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Answer:

191.5

Step-by-step explanation:

Answer:

4

--

3

Step-by-step explanation:

Rate of Change via a table should be

f(x2)-f(x1)

-------------

x2 - x1

In this problem they indicated X2 is 36 and X1 is 18

At 36, F(X) is 61 and for 18, it's 37

Now to plug in...

61 - 37

----------

36 - 18

That boils down to

24

----

18

If we want to simplify it;

4

--. or. 1.333

3

Answer: A quadratic of the form $ax^2 + bx + c$ has rational roots if and only if its discriminant, $b^2 - 4ac$, is a perfect square. In this case, the discriminant is $(20)^2 - 4(3)(c) = 400 - 12c$. So, we need to find the positive integers $c < 100$ that make $12c$ a perfect square.

The perfect squares that are less than $100$ are $1,4,9,16,25,36,49,64,81$, so the possible values for $c$ are $33,44,55,66,77,88$.

So, the positive integers $c$, with $c < 100$, that make the quadratic have rational roots are $33,44,55,66,77,88$

Step-by-step explanation:

Answer: 38

Step-by-step explanation:

You can split this shape into 2 rectangles. The area of the two rectangles = 5 * 4 + 6 * 3

= 20 + 18

= 38

A polynomial equation of the second degree, or a quadratic, must contain at least one squared term to be considered a quadratic.

Quadratic equations or quadratic functions. A polynomial equation of the second degree, or a quadratic, must contain at least one squared term to be considered a quadratic. Equations using quadratics is another name for it. The quadratic equation is expressed in its general form as ax2 + bx + c = 0.

For instance, 6x2 + 11x - 35 = 0, 2x2 - 4x - 2 = 0, 2x2 - 64 = 0, x2 - 16 = 0, x2 - 7x = 0, 2x2 + 8x = 0, etc. are examples of quadratic equations.

Three kinds of quadratics are frequently employed:

Standard Form: y = an x 2 + b x + c y = an x 2 + b x + c

y = a (x r 1, x r 2) is the factored form. y=a(x-r 1)(x-r 2) y=a(x−r1)(x−r2)

Vertex Formula: y=a (x h) 2 + k y=a (x-h)2 + k y=a (x-h) 2+k.

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Answer:

the probability of randomly selecting the chair and the vice chair is 10%.

Step-by-step explanation:

There are a total of 5 members on the health services committee, and 2 of them will be chosen to serve as the chair and vice chair, respectively.

The probability of randomly selecting the chair out of the 5 members is 2/5, or 40%.

Once the chair is selected, there are 4 members remaining, and only one of them can serve as the vice chair. Therefore, the probability of randomly selecting the vice chair out of the remaining 4 members is 1/4, or 25%.

To find the probability of randomly selecting the chair and the vice chair, we need to multiply the individual probabilities of selecting each position, which is (2/5) * (1/4) = 2/20 = 1/10 = 10%.

So, the probability of randomly selecting the chair and the vice chair is 10%.

Take the original data and divide it by the standard deviation to determine the z-scores. X is a symbol for the relevant data point. For the population from which you selected your sample, mu and sigma stand in for the mean and standard deviation.

In terms of standard deviations above or below the mean, a data point's z-score quantifies this exact distance.

A z-score is calculated using the following formula:

data point = mean standard deviation

Data point means with standard deviation equal to z

The same equation is given below in symbol form:

z=  x−μ / σ

Some significant z-score details are as follows:

An elevated z-score indicates that the data point is.

When a data point has a negative z-score, it is below average.

The data point is considered to be roughly average if the z-score is near to 0.00.

If a data point's z-score is higher or lower than 3 33 or 3 3minus, the data point is deemed uncommon.

At Almond, the average score on a history midterm is

= 85 = 85mu, which is equivalent to 85 with a standard deviation of

= 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2

On the test, Michael received a score of 86.866.668.

Calculate Michael's exam grade in Z-score form.

His Grade = Mean Grade Standard Deviation

= 86 − 85 / 2

= 1 /2 = 0.5 z z z

= standard deviation of his grade and mean grade.

= 2 / 86−85

= 2 / 1 =0.5.

The z-score for Michael is 0.5, 0.50, and 5. He received a grade that was half a standard deviation higher than the mean.

​

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Total distance travelled by the cyclist is 131/40 km in fraction.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.

The three main sorts of fractions are as follows. Proper fractions, improper fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categorize its kinds based on these two parameters.

Total distance travelled by the cyclist is 7/8 + 9/10 + 3/2 = 131/40 km

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We can conclude that the division property of equality was done between step 4 and step 5.

What is linear equation ?

Linear equation can be defined as the equation in which the highest degree is one.

The Division Property of Equality states that when both sides of an equation are divided by the same nonzero number, both sides remain equal.

That is, if a, b, and c are real numbers such that a = b and c ≠0, then  

a/c = b/c

At step 4: The equation was -6x = 57

To move to step 5, Paula had to divide both sides by the co-efficient of x (-6) in order to get the value of x. See below

-6x = 57

---- Divide both sides by -6 (Step 4)

-6x / -6  = 57 / -6

---- (Intermediary between step 4 and 5)

x = -9.5

----- Step 5

Hence, we can conclude that the division property of equality was done between step 4 and step 5

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The  Pinewoods Trail is longer than the Outlook Trail.

The definition of a fraction is a portion of a whole. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin.

Given the length of Lake Trail = 4 and 3/5 mile

length of Lake Trail = 23/5 miles

length of Outlook Trail = 5 and 5/6 mile

length of Outlook Trail = 35/6 miles

length of Pinewoods Trail = 1 and 3/10 miles longer than Lake Trail

length of Pinewoods Trail = 33/10 + 23/5

length of Pinewoods Trail = (33 + 46)/10

length of Pinewoods Trail = 79/10 miles

comparing the length of  Outlook Trail  and  Pinewoods Trail,

which is 35/6 and 79/10 miles respectively,

the common denominator for both is 30,

35/6 = (35*5)/(6*5)

35/6 = 175/30

and 79/10 = (79*3)/(10*3)

79/10 = 273/30

here 273/30 > 175/30

Hence  Pinewoods Trail is longer.

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The coordinates of the hooks in three-dimensional space are found and the mid-point of the string is recognised as (4.5, 6, 7.75).

What is meant by three-dimensional space?

A three-dimensional space in geometry is a mathematical structure where a point's location depends on three different values.

For this question, we are considering the east of origin as the positive x-axis, the above origin as the positive z-axis and the north of the origin as the positive y-axis.

a)  For the first hook there is no y-axis, it is hung in the xz plane.

So the coordinates are (4,0,7.5)

b) The second hook coordinates are given as (5, 12,8)

c) The point on the string which joins the hook, which is halfway between the hooks can be found using the mid-point formula.

x= (x1 + x2)/2 = (4+5)/2 = 4.5

y = (y1 + y2) /2 = (0+12) / 2 = 6

z = (z1+z2) / 2 = (7.5 + 8) /2 = 7.75

Therefore the mid-point of the string is (4.5, 6, 7.75).

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a) The discount on the loan is $1,862.

b) The amount of money the borrower received on the discount loan is $11,438.

c) The true interest rate paid on the discounted loan is 4.1%.

A discount loan is a type of loan in which the interest (cost of borrowing) is deducted upfront or at the time the loan is granted.

The implication of getting a discount loan is that the amount received is less than the principal amount because the grantor has reduced it by interest and other fees (finance charges).

The principal = $13,300

Discount rate = 3¹/₂%

Time = 4 years

Discount = $1,862 ($13,300 x 3.5% x 4)

Amount received = $11,438 ($13,300 - $1,862)

Real interest rate = 4.1% ($1,862/$11,438 x 100)/4

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so hmm £36000 will be split, hmmm let's call the ratios "a,b and c", so the amount will be split in ratios of a : b : c, which means we'll be dividing the 36000 bucks by (a + b + c) and distribute accordingly, let's do that, hmm let's convert also all those mixed fractions to improper fractions.

[tex]\stackrel{mixed}{2\frac{3}{4}}\implies \cfrac{2\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{11}{4}} ~\hfill \stackrel{mixed}{1\frac{1}{2}} \implies \cfrac{1\cdot 2+1}{2} \implies \stackrel{improper}{\cfrac{3}{2}} \\\\\\ \stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} ~\hfill \boxed{\cfrac{11}{4}+\cfrac{3}{2}+\cfrac{9}{4}\implies \cfrac{13}{2}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{36000}{~~ \frac{13 }{2 } ~~}\implies 36000\cdot \cfrac{2}{13}\implies \cfrac{72000}{13} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{Alex}{\cfrac{11}{4}\cdot \cfrac{72000}{13}}~~ : ~~\stackrel{Bill}{\cfrac{3}{2}\cdot \cfrac{72000}{13}}~~ : ~~\stackrel{Claire}{\cfrac{9}{4}\cdot \cfrac{72000}{13}}\implies \stackrel{Alex}{\cfrac{198000}{13}}~~ : ~~\stackrel{Bill}{\cfrac{108000}{13}}~ : ~\stackrel{Claire}{\cfrac{162000}{13}} \\\\\\ ~\hfill \stackrel{Alex}{15230\frac{10}{13}}~~ : ~~\stackrel{Bill}{8307\frac{9}{13}}~ : ~\stackrel{Claire}{12461\frac{7}{13}}~\hfill[/tex]

Answer:

102

Step-by-step explanation:

34x3=102

The histogram that accurately summarizes the data in this problem is given by the second image presented at the end of the answer.

The histogram of a data-set shows the number of times that each item was observed in the data-set.

From the first image given at the end of the answer, the absolute frequencies are given for each observation, which is the height of each bin of the histogram.

The problem is given by the first image presented at the end of the answer.

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